Develop an Assessment Exercise



Develop an Assessment Exercise

FDN 5560 Classroom Assessment

Dr. George Olson

Harry

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Develop an Assessment 1: Identify Learning Targets

Quadratic equations and functions will be the focus of this instructional unit. Quadratics is a major component for the North Carolina Algebra 1 curriculum as defined by the North Carolina Standard Course of Study. The target audience will be English Language Learners (ELL) that are primarily in the 9th and 10th grade. These students are in their second semester of a year-long Algebra 1 course. The course will conclude with a state administered end of course examination. The examination focuses more on higher order thinking skills rather than recalling facts. The development of this assessment, with anticipation, will assist me in allowing my students to develop those higher order thinking skills.

The unit focuses primarily on graphing quadratic equations, but will also include retrieving prior knowledge from the students in the areas of graphing linear equations, solving equations and factoring equations. Unraveling quadratic equations can be a very difficult unit for students, especially ELL students, but it is also one that can be detrimental for them on the end of course exam and in more advance math classes. This is a unit that has the capability of tying many Algebra concepts together.

The target goals are designed to scaffold learning of the various concepts. Mastery of the goals must be accomplished before moving on to the next goal. The initial assessments of each target goal will be more knowledge based and skill building, where as, the latter assessments will be sequenced to more difficult tasks of analysis and application. It should be noted that the number of target goals is dependent upon the importance of this particular unit as well as the target audience of ELL students.

1. The student will be able to define key vocabulary terms associated with quadratics. I would rather see a statement about what the student will do.

This is a lower level knowledge and comprehension skill. This target goal is essential because it provides knowledge of the terminology that is utilized when graphing and solving quadratic equations. Matching two homogenous lists of terms and definitions will be used to evaluate this target goal. The comprehension of these terms is necessary for the mastery of latter goals in this unit.

2. Given a TI-83 Plus graphing calculator, the student will be able to graph a quadratic function.

The learning target is a transitional-level goal since it relates to skill building. This is a target that correlates to basic prior knowledge acquired in simple linear graphing concepts. The target goal requires specific calculator skill and the ability to manipulate the keystrokes. Multiple choice responses will be used to evaluate this target goal. Calculator manipulation will prove to be an important skill for concluding learning targets.

3. Given a TI-83 Plus graphing calculator, the student will be able to manipulate the coefficients and constants of a quadratic equation.

The learning target is an intermediate-level goal that includes the ability to alter the coefficients and constants of a standard quadratic function. Prior learning of calculator manipulation will aid in the ability to make predictions about transformations in graphs dependent upon modifying input. This target will be assessed by using short answer response.

4. Given a TI-83 Plus graphing calculator, the student will be able determine the vertex of a quadratic equation.

The learning target is an intermediate-level goal that includes the ability to determine the vertex of a quadratic using the TI-83 Plus graphing calculator. Utilization of the calculator must be achieved to receive the desired outcome. The target goal will be assessed with binary multiple choice as well as short answer response.

5. Given a TI-83 Plus graphing calculator, the student will be able visualize the number of x intercepts of a quadratic function.

This is a lower level knowledge and comprehension skill. The number of solutions of a quadratic equation will be established after observing the graphed function. Mastery will be determined by using a multiple choice assessment with three choices. Comprehension of this goal proves to be detrimental when solving quadratic equations.

6. Given a TI-83 Plus graphing calculator, the student will be able pinpoint the solutions of a quadratic function.

The student is applying basic knowledge learned in earlier targets while also depending on teacher guided input. The learning goal relies heavily on specific calculator skills. This target will be assessed by using short answer response.

7. The student will be able to solve a quadratic equation using the factoring method.

This is an application target that correlates to basic prior knowledge acquired in previously learned units of factoring equations as well as solving equations. The target goal can be used in conjunction with Learning Target #6 to compare exactness of the solution(s). The assessment of this goal will be somewhat unique. I will provide the solutions while the students must generate the quadratic function.

8. The student will be able to solve a quadratic equation using the quadratic formula.

This is an application target that correlates to basic prior knowledge acquired in previously learned units of evaluating radicals. The target goal can be used in conjunction with Learning Target #6 to compare exactness of the solution(s). The assessment of this goal will be with short answer response.

9. Using a real world application, the student will be able to develop and solve quadratic functions as well as be able to make a decision on choosing an appropriate method for solving a quadratic function.

This learning target will conclude the unit on quadratics and is a higher-order learning target. The student must first formulate a hypothesis of a given scenario related to projectile objects. The scenario is then demonstrated via internet resource. The student is given immediate feedback on their response. The student then solves an assortment of quadratics using a variety of methods learned in previous learning targets. Finally the student will name three methods that can be use to solve quadratics and critique the limitations of each in a short essay. This unit will prepare the student not only to be able to comprehend the methods of solving quadratics but will also prepare the student to make decisions on choosing an appropriate method. The target goal will be assessed by several means. First, the answers to precise tables and graphs will be assessed by student constructed illustrations. A short essay will also be used to critique methods of solving quadratics. This essay should not be more than two pages. The teacher will be able to conclude student achievement using these two methods. Student achievement in an essential unit of quadratics will lead to success in future related mathematics courses.

References

Pearson Education, INC., (2007). Algebra: Quadratic Functions

and Equations. Retrieved March 11, 2007, Web site:



Popham, W.J. (2005). Classroom assessment: What teachers need to

know. Boston: Pearson, Allyn, and Bacon.

North Carolina Department of Public Instruction. (2003). North

Carolina Standard Course of Study for Algebra 1. Retrieved

February 20, 2007 from



Develop an Assessment 2: Specifications for a Test

9-12 Algebra 1 – Quadratic Functions

Learning Target #5: (knowledge and comprehension) Given a TI-83 Plus graphing calculator, the student will be able discover the number of x intercepts of a quadratic function.

Test Specifications: Given 15 multiple choice items with three choices, the student will be able to identify the number of solutions upon graphing a quadratic equation on the TI-83 Plus calculator. The students will be provided with a quadratic function and the choices of 0, 1, or 2. The student will graph the function, manipulate the x-axes and determine the number of solutions by circling the correct choice.

Test Directions: Graph each quadratic equation and then circle the correct number of solutions for that function.

Sample Items:

1. y = x^2 – 4x + 3 0 1 2

2. y = x^2 – 2x + 1 0 1 2

3. y = x^2 + x + 1 0 1 2

Instructions for writing similar items:

➢ Confirm that each question measures the learning target.

➢ Confirm that each item has a correct answer.

➢ Keep item length similar for both categories.

➢ Include only one equation in each item.

➢ Confirm that each equation is written in standard form.

There should be a statement concerning relevant or acceptable content. What level of difficulty? Etc.

Scoring Plan: Total number of questions and points – 15.

Each question will be worth 1 point. Mastery of this learning target will be defined by the student’s ability to answer 12 of the 15 items correctly.

Develop an Assessment 2: Specifications for a Test

9-12 Algebra 1 – Quadratic Functions

Learning Target #3: (intermediate application) Given a TI-83 Plus graphing calculator, the student will be able to manipulate the coefficients and constants of a quadratic equation.

Test Specifications: Given 20 short answer items and a graphing calculator, the students will correctly be able to describe the transformations in the graph of a parent equation to one in which the coefficients have been manipulated. Transformations include opening up or down, wide or narrow, shift up or down, and shift left or right.

Test Directions: Graph each quadratic equation on the same screen and compare the graph to the parent graph of y= x^2. Briefly describe the changes in the space provided. Transformations include opening up or down, wide or narrow, shift up or down, and shift left or right.

Again, what is acceptable (or accessible) content?

Sample Items:

Functions Transformations on Graph

1. y = x^2

y = -x^2 ____________________

2. y = x^2

y = x^2 – 3 ____________________

3. y = x^2

y = 1/2x^2 ____________________

Instructions for writing similar items:

➢ Structure the item so that a response should be concise.

➢ Make sure all blanks for all items are equal in length.

➢ Ensure all blanks are equal in length.

➢ Place answer blanks immediately after the item.

Scoring Plan: Total number of questions and points – 20.

Each question will be worth 1 point. Mastery of this learning target will be defined by the student’s ability to answer 17 of the 20 items correctly.

Develop an Assessment 3: Craft a Performance Assessment

9-12 Algebra 1 – Quadratic Functions

Learning Target: Using a real world application, the student will be able to develop and solve quadratic functions as well as be able to make a decision on choosing an appropriate method for solving a quadratic function.

This learning target will conclude the unit on quadratics and is a higher-order learning target. The student must first formulate a hypothesis of a given scenario related to projectile objects. The scenario is then demonstrated via internet resource. The student is given immediate feedback on their response. The student then graphs an assortment of quadratics using a variety of methods learned in previous learning targets. Finally the student will name three methods that can be use to solve quadratics and critique the limitations of each in a short essay. This unit will prepare the student not only to be able to comprehend the methods of solving quadratics but will also prepare the student to make decisions on choosing an appropriate method. The target goal will be assessed by several means. First, the answers to precise tables and graphs will be assessed by student constructed diagrams. A short essay will also be used to critique methods of solving quadratics. This essay should not be more than one page. The teacher will be able to conclude student achievement using these two methods. Student success in a significant unit such as quadratics will lead to success in future related mathematics courses.

Assignment

Determine how the graph of a quadratic equation can help us to answer questions about the height of an object. Determine three methods of solving a quadratic equation and decide which method is most appropriate for a given situation.

Learning Target: Using a real world application, the student will be able to develop and solve quadratic functions as well as be able to make a decision on choosing an appropriate method for solving a quadratic function.

Task Structure: The student will be presented with scenarios dealing with projectile functions. The student will specifically 1) graph the equations, 2) find the x intercepts of the equations, 3) solve the identical equations by factoring and by evaluating with the quadratic formula, and 4) name three methods that can be used to solve quadratic equations and describe the limitations of each of these methods in a one page essay. An excellent score requires 1) graphs and tables that are clear 2) all problems are completed showing proper steps 3) a concise essay, (one full page) providing a detailed explanation of 3 methods of solving quadratic functions, 4) typically, uses an efficient and effective strategy to solve the problem(s), and 5) the work is presented in a neat, clear, organized fashion that is easy to read. To show proficiency 1) graphs and tables are clear and easy to understand, 2) all but 1 of the problems is complete, 3) a short essay (3/4 of a page) providing a vague explanation of 3 methods of solving quadratic functions, 4) uses an efficient and effective strategy to solve the problems most of the time, and 5) the work is presented in a neat and organized fashion that is usually easy to read. Scores will be determined on a 4 point scale as provided on the rubric.

Directions for Assessment:

The student will be directed to the following website .

The student must first formulate a hypothesis of a given scenario related to projectile objects. The scenario is then demonstrated via internet resource. The student is given immediate feedback on their response. The student will graph an assortment of quadratics using a variety of methods learned in previous learning targets. Finally the student will name three methods that can be use to solve quadratics and critique the limitations of each in a short essay. This unit will prepare the student not only to be able to comprehend the methods of solving quadratics but will also prepare the student to make decisions on choosing an appropriate method. Student success in a significant unit such as quadratics will lead to success in future related mathematics courses.

|Category | Excellent |Proficient |Below Standard |Well Below Standard |

|Graphs and Tables |Graphs and tables are |Graphs and tables are |Graphs and tables are |Graphs and tables are |

| |clear and greatly add to |clear and easy to |somewhat difficult to |difficult to understand or |

| |the student's |understand. |understand. |are not used. |

|Not sure what these hve to do |understanding of the | | | |

|with the LT |procedure(s). | | | |

| | | | | |

|4, 3, 2, 1 | | | | |

|Completeness of Problems |All problems are completed|All but 1 of the |All but 2 of the problems |None of the problems are |

| |showing proper steps |problems is completed. |are completed. |completed. |

|4, 3, 2, 1 | | | | |

|Essay |Concise, (one full page) |Short essay, (3/4 of a |Short essay, (1/2 of a |Incomplete essay (one |

| |providing a detailed |page) providing a vague|page) providing a sketchy |Paragraph) providing no |

| |explanation of 3 methods |explanation of 3 |explanation of 3 methods of|explanation of 3 methods of |

| |of solving quadratic |methods of solving |solving quadratic |solving quadratic functions. |

| |functions. |quadratic functions. |functions. | |

| | | | | |

| | | | | |

|4, 3, 2, 1 | | | | |

|Strategies/Reasoning |Typically, uses an |Uses an efficient and |Sometimes uses an effective|Rarely uses an effective |

| |efficient and effective |effective strategy to |strategy to solve problems,|strategy to solve problems. |

| |strategy to solve the |solve the problem most |but does not do it | |

| |problem(s). |of the time. |consistently. | |

| | | | | |

|4, 3, 2, 1 | | | | |

|Neatness and organization |The work is presented in a|The work is presented |The work is presented in an|The work appears sloppy and |

| |neat, clear, organized |in a neat and organized|organized fashion but may |unorganized. It is hard to |

| |fashion that is easy to |fashion that is usually|be hard to read at times. |know what information goes |

| |read. |easy to read. | |together. |

| | | | | |

| | | | | |

|4, 3, 2, 1 | | | | |

|TOTAL POINTS | | | | |

| | | | | |

Each category will be rated on a 4-1 point scale. Four points for excellent, 3 points for proficient, 2 points for below standard and 1 point for well below standard.

A final score will be assessed from a sum of each category total. Each performance assessment will be assigned an overall score of 0-20. Scores of 1-5 rate well below standard, 6-10 rate below standard, 11-15 rate proficient, and 16-20 rate excellent.

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